Financial institutions, resource-based corporations, trading organizations, governments, and others may employ risk management systems and methods to measure risk associated with portfolios comprising credit-risky instruments, such as for example, the trading book of a bank. Accurately evaluating the risk associated with a portfolio of instruments may assist in the management of the portfolio. For example, it may allow opportunities for changing the composition of the portfolio in order to reduce the overall risk or to achieve an acceptable level of risk to be identified.
Evaluating the risk associated with a portfolio is a non-trivial task, as instruments (e.g. securities, loans, corporate bonds, credit derivatives, etc.) in the portfolio can be of varying complexity, and may be subject to different types of risk. An instrument may lose value due to adverse changes in market risk factors, for example. An instrument may also lose value due to changes in the credit state (e.g. a downgrade) of the counterparty associated with the instrument, for example.
Consider, by way of illustration, that the price of a bond generally declines as interest rates rise. Interest rates are examples of market risk factors. Further examples of market risk factors may include equity indices, foreign exchange rates, and commodity prices.
Also consider, by way of illustration, that a AA-rated counterparty associated with an instrument of the portfolio may transition to a credit state with a lower rating (e.g., B) or one with a higher rating (e.g., AAA), resulting in an accompanying decrease or increase, respectively, in the values of its financial obligations. These changes may, in turn, affect the values of the associated instrument. In an extreme case, a counterparty may default, typically leaving creditors able to recover only some fraction of the value of their instruments with the counterparty.
Credit state migrations (e.g. transitions to different credit states) may be determined by evaluating movements of a creditworthiness index calculated for a specific counterparty. The creditworthiness index may be based on values of a number of systemic credit drivers that generally affect all counterparties and of an idiosyncratic credit risk factor associated with the specific counterparty.
The systemic credit drivers may comprise macroeconomic variables or indices, such as for example, gross domestic product (GDP), inflation rates, and country/industry indices. Accordingly, these systemic credit drivers generally provide a credit correlation between different counterparty names in a portfolio. In contrast, each idiosyncratic credit risk factor is a latent variable independently associated with a specific counterparty name in the portfolio. Accordingly, these idiosyncratic credit risk factors may also be referred to as counterparty-specific credit risk factors herein.
In general, changes to market risk factors and systemic credit drivers tend to be correlated (i.e. in statistical terms, the market risk factors and systemic credit drivers are co-dependent, not independent). Accordingly, many modern risk management systems and methods may be expected to employ methodologies that integrate market and credit risk (e.g. by ensuring that such co-dependence is reflected in the computation of risk measures associated with a portfolio) in order to more accurately assess the financial risks associated with portfolios of interest. Furthermore, approaches that integrate market and credit risk have been further validated by the advent of the International Standard for Banking Regulations Basel II.
To evaluate risk associated with a portfolio, at least some risk management systems and methods perform simulations in which a portfolio of instruments evolves under a set of scenarios (e.g. a set of possible future outcomes, each of which may have an associated probability of occurrence) over some specified time horizon. The losses (or gains) that a portfolio of interest may incur over all possible scenarios might be represented by a loss distribution. With knowledge of the loss distribution associated with the portfolio, it is possible to compute a risk measure for the portfolio of interest.
However, as it is not possible to determine the exact loss distribution analytically, it may be approximated by an empirical distribution. By way of simulation, under each scenario, an individual loss sample may be generated. The scenario used to generate a given loss sample may represent a certain specific set of market and credit conditions, identified by particular sampled values of market risk factors, systemic credit drivers and/or idiosyncratic credit risk factors defined for the respective scenario.
The loss samples generated under a plurality of scenarios may be used to generate the empirical distribution that approximates the actual loss distribution. Accordingly, it will be understood that the larger the number of scenarios used in the simulation and thus the larger the number of loss samples generated, the more accurate the approximation of the actual loss distribution will be.
Estimates of risk measures associated with the portfolio may then be computed based on the empirical distribution that approximates the actual loss distribution. In this regard, the quality of the estimated measurement of risk will also depend on the number of loss samples generated. It will be understood that the individual loss samples may also be referred to collectively as a “loss sample”, and the number of individual loss samples may be referred to as the size of the “loss sample”.
Some known risk management systems generate loss samples according to a methodology that may be classified as a “simple sampling” approach. In accordance with a “simple sampling” approach, to generate a given loss sample, a corresponding market risk factor sample, systemic credit driver sample, and idiosyncratic credit risk factor sample is generated. In order to integrate market and credit risk, the market risk factors and systemic credit drivers are assumed to evolve in accordance with a pre-specified co-dependence structure. It will be understood that in order to obtain N loss samples using this approach, N market risk factor samples, N systemic credit driver samples, and N idiosyncratic credit risk factor samples will be generated in the simulation for a portfolio of interest. Accordingly, the “simple sampling” approach may be considered to be an example of a “brute force” approach to generating loss samples for the portfolio in the simulation.
Some other known risk management systems generate loss samples according to a methodology that may be classified as a “two-tier” approach. In accordance with a “two-tier” approach, a joint sample of market risk factors and systemic credit drivers is combined with multiple samples of idiosyncratic credit risk factor values to obtain multiple loss samples. In order to integrate market and credit risk, the market risk factors and systemic credit drivers are assumed to evolve in accordance with a pre-specified co-dependence structure. The “two-tier” approach attempts to reduce the number of market risk factor and systemic credit driver samples needed to obtain N loss samples. However, it will be understood that if joint samples of market risk factors and systemic credit drivers are employed, where there is a need to consider a larger number of samples of one type of risk factor (e.g. systemic credit drivers), then a larger number of samples of the other type of risk factor (e.g. market risk factors) will be required.
Yet other known risk management systems do not attempt to integrate market and credit risk when evaluating risk associated with a portfolio. For example, some known risk management systems may derive a loss distribution analytically, ignoring the correlation between changes in market risk factors and systemic credit drivers that exists, in reality.